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Equivalent matrices

From Encyclopedia of Mathematics - Reading time: 1 min

A and B over a ring R

Matrices such that A can be transformed into B by a sequence of elementary row-and-column transformations, that is, transformations of the following three types: a) permutation of the rows (or columns); b) addition to one row (or column) of another row (or column) multiplied by an element of R; or c) multiplication of a row (or column) by an invertible element of R. Equivalently, B is obtained from A by multiplication on left or right by a sequence of matrices each of which is either a) a permutation matrix; b) an elementary matrix; c) an invertible diagonal matrix.

Equivalence in this sense is an equivalence relation.


How to Cite This Entry: Equivalent matrices (Encyclopedia of Mathematics) | Licensed under CC BY-SA 3.0. Source: https://encyclopediaofmath.org/wiki/Equivalent_matrices
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